Periodic ILW equation with discrete Laplacian

Abstract

We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass zeta-function. Using Sato's formulation, we show the integrability and construct some special solutions. An elliptic solution is also obtained. We present a conjecture based on a Poisson structure that it gives an alternative description of this integrable hierarchy. We note that this Poisson algebra in turn is related to a quantum algebra related with the family of Macdonald difference operators.

17 pages. To appear in J. Phys. A: Math. Theor

References in corpus (2)

• A Commutative Family of Integral Transformations and Basic Hypergeometric Series. I. Eigenfunctions
• The ILW hierarchy

Cited by in corpus (5)

• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian
• Lax operator for Macdonald symmetric functions
• On Dimensional Transmutation in 1+1D Quantum Hydrodynamics
• Generalized ILW hierarchy: Solutions and limit to extended lattice GD hierarchy